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        <title>API docs for &ldquo;sympy.thirdparty.mpmath.functions2&rdquo;</title>
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        <body><h1 class="module">Module s.t.m.functions2</h1><span id="part">Part of <a href="sympy.thirdparty.mpmath.html">sympy.thirdparty.mpmath</a></span><div class="toplevel"><div><p>Numerical implementations of special functions (gamma, ...)</p>
</div></div><table class="children"><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2._fix">_fix</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2._re">_re</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2._im">_im</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2._calc_spouge_coefficients">_calc_spouge_coefficients</a></td><td><div><p>Calculate Spouge coefficients for approximation with parameter a.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2._get_spouge_coefficients">_get_spouge_coefficients</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2._spouge_sum">_spouge_sum</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2.gamma">gamma</a></td><td><div><p>Returns the gamma function of x. Raises an exception if</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2.factorial">factorial</a></td><td><div><p>Returns the factorial of x, defined in terms of the gamma</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2._lower_gamma_series">_lower_gamma_series</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2.lower_gamma">lower_gamma</a></td><td><div><p>Returns the lower incomplete gamma function gamma(a, z)</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2.upper_gamma">upper_gamma</a></td><td><div><p>Returns the upper incomplete gamma function Gamma(a, z)</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2.erf">erf</a></td><td><div><p>Returns the error function of x.</p>
</div></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2._zeta_coefs">_zeta_coefs</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2._logk">_logk</a></td><td><span class="undocumented">Undocumented</span></td></tr><tr class="function"><td>Function</td><td><a href="#sympy.thirdparty.mpmath.functions2.zeta">zeta</a></td><td><div><p>Returns the Riemann zeta function of s.</p>
</div></td></tr></table>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2._fix">_fix(x, prec):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2._re">_re(s):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2._im">_im(s):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2._calc_spouge_coefficients">_calc_spouge_coefficients(a, prec):</a></div>
            <div class="functionBody"><div><p>Calculate Spouge coefficients for approximation with parameter a. Return
a list of big integers representing the coefficients in fixed-point form 
with a precision of prec bits.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2._get_spouge_coefficients">_get_spouge_coefficients(prec):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2._spouge_sum">_spouge_sum(x, prec, a, c):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2.gamma">gamma(x):</a></div>
            <div class="functionBody"><div><p>Returns the gamma function of x. Raises an exception if x == 0, -1, -2, 
-3, ... where the gamma function has a pole.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2.factorial">factorial(x):</a></div>
            <div class="functionBody"><div><p>Returns the factorial of x, defined in terms of the gamma function for 
non-integer x. An exception is raised if x is a negative integer.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2._lower_gamma_series">_lower_gamma_series(are, aim, zre, zim, prec):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2.lower_gamma">lower_gamma(a, z):</a></div>
            <div class="functionBody"><div><p>Returns the lower incomplete gamma function gamma(a, z)</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2.upper_gamma">upper_gamma(a, z):</a></div>
            <div class="functionBody"><div><p>Returns the upper incomplete gamma function Gamma(a, z)</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2.erf">erf(x):</a></div>
            <div class="functionBody"><div><p>Returns the error function of x.</p>
</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2._zeta_coefs">_zeta_coefs(n):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2._logk">_logk(k):</a></div>
            <div class="functionBody"><div class="undocumented">Undocumented</div></div>
            </div>
            <div class="function">
            <div class="functionHeader">def <a name="sympy.thirdparty.mpmath.functions2.zeta">zeta(s):</a></div>
            <div class="functionBody"><div><p>Returns the Riemann zeta function of s.</p>
</div></div>
            </div></body>
        